I work for a foreign corporation. They don't care whether or not I have a SSN (I'm an LLC as far as the US gov't is concerned). If I didn't have the magic ID card, they wouldn't give a damn. I do the work, they pay me. Staying out of US tax court is my problem, not theirs.
I'm starting to see more people in my profession (engineering) working for overseas bosses because of the onerous tax and other regulations placed on contractors in this country. I'm sure more will follow.